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Chapter 16: Problem 4

What is the temperature \(1.0 \mathrm{K}\) on the Fahrenheit scale?

Short Answer

Expert verified
1.0 K is -457.87掳F.

Step by step solution

01

Understand the Conversion Formula

To convert a temperature from Kelvin to Fahrenheit, we use the formula: \[ T(掳F) = T(K) \times \frac{9}{5} - 459.67 \] This formula accounts for both the ratio of the degree intervals and the difference in the zero points of Kelvin and Fahrenheit scales.
02

Substitute the Given Temperature

We are given the temperature as 1.0 K. Substitute this value into the conversion formula:\[ T(掳F) = 1.0 \times \frac{9}{5} - 459.67 \]
03

Perform the Multiplication

Calculate the multiplication part of the formula:\[ 1.0 \times \frac{9}{5} = 1.8 \] This result represents the temperature in degrees Fahrenheit before subtracting 459.67.
04

Subtract from Fahrenheit Zero Point

Finish the calculation by subtracting 459.67 from the result of the multiplication:\[ T(掳F) = 1.8 - 459.67 = -457.87 \]
05

Interpret the Result

The final result of -457.87掳F means the temperature of 1.0 K is quite cold in Fahrenheit scale, confirming that Kelvin represents absolute temperature where 0 K is absolute zero.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kelvin to Fahrenheit conversion
Understanding how to convert temperatures from Kelvin to Fahrenheit can be quite straightforward once you get the hang of it. Here's how it works: the formula for conversion is \[ T(掳F) = T(K) \times \frac{9}{5} - 459.67 \]. This formula might look complex at first, but it's mainly adjusting for the different scales used by Kelvin and Fahrenheit.
  • The term \( T(K) \times \frac{9}{5} \) converts the temperature from Kelvin's scale intervals to those of Fahrenheit.
  • The subtraction of 459.67 accounts for the offset between the two scales' zero points.
Using this formula, you can easily convert any temperature from the Kelvin scale to the Fahrenheit scale, making sense of temperatures even when diving deep into scientific contexts.
temperature scales
Temperature scales can sometimes seem confusing, but understanding them helps make temperature discussions much simpler. The main scales used today are Kelvin, Celsius, and Fahrenheit.
  • Kelvin Scale: Widely used in scientific experiments, the Kelvin scale starts at absolute zero and increases without using negative numbers.
  • Celsius Scale: This is the most commonly used scale in everyday life; water freezes at 0掳C and boils at 100掳C.
  • Fahrenheit Scale: Mainly used in the United States, water freezes at 32掳F and boils at 212掳F.
Each scale has its own applications and features uniquely suited to different needs. Understanding these differences is key, especially in scientific and engineering contexts, where precision is critical.
absolute zero
Absolute zero is an essential concept in thermodynamics and physics. It represents the lowest possible temperature, equivalent to 0 Kelvin or -273.15掳C. At this point, the particles in a substance have minimal vibrational motion, signifying the theoretical complete absence of thermal energy.
  • Absolute Zero in Science: This concept is crucial in understanding thermodynamics and helps scientists explore quantum physics.
  • Measurements: While absolute zero is unattainable in practice, advancements in cooling technology allow scientists to get close.
The notion of absolute zero not only aids our understanding of temperature scales but also forms the backbone of calculations involving entropy and enthalpy, pivotal in scientific research.

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Most popular questions from this chapter

A sheet of aluminum has a circular hole with a diameter of \(10.0 \mathrm{cm} .\) A \(9.99-\mathrm{cm}\) -long steel rod is placed inside the hole, along a diameter of the circle, as shown in Figure \(16-21\). It is desired to change the temperature of this system until the steel rod just touches both sides of the circle. (a) Should the temperature of the system be increased or decreased? Explain. (b) By how much should the temperature be changed?

Two metal rods-one lead, the other copper-are connected in series, as shown in Figure \(16-18\). These are the same two rods that were connected in parallel in Example \(16-7 .\) Note that each rod is \(0.525 \mathrm{m}\) in length and has a square cross section \(1.50 \mathrm{cm}\) on a side. The temperature at the lead end of the rods is \(2.00^{\circ} \mathrm{C} ;\) the temperature at the copper end is \(106^{\circ} \mathrm{C} .\) (a) The average temperature of the two ends is \(54.0^{\circ} \mathrm{C}\). Is the temperature in the middle, at the lead- copper interface, greater than, less than, or equal to \(54.0^{\circ} \mathrm{C}\) ? Explain. (b) Given that the heat flow through each of these rods in \(1.00 \mathrm{s}\) is \(1.41 \mathrm{J}\), find the temperature at the lead- copper interface.

Two identical objects are placed in a room at \(21^{\circ} \mathrm{C}\). Object 1 has a temperature of \(98^{\circ} \mathrm{C}\), and object 2 has a temperature of \(23^{\circ} \mathrm{C} .\) What is the ratio of the net power emitted by object 1 to that radiated by object \(2 ?\)

Find the heat that flows in 1.0 s through a lead brick \(15 \mathrm{cm}\) long if the temperature difference between the ends of the brick is \(9.5 \mathrm{C}^{\circ} .\) The cross-sectional area of the brick is \(14 \mathrm{cm}^{2}\).

Two bowls of soup with identical temperatures are placed on a table. Bowl 1 has a metal spoon in it; bowl 2 does not. After a few minutes, is the temperature of the soup in bowl 1 greater than, less than, or equal to the temperature of the soup in bowl \(2 ?\)
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